5. The Mathematics of the Infinitely Small

09/23/16 • 13 min

Having looked at the infinite in philosophical and theological terms, it’s time to view it through the lens of mathematics.

Adrian Moore introduces us to the pivotal role mathematics has played in the quest to understand the infinite.

He begins by enlisting the help of very modern technology and considering the real question put by an 11 year old boy - what is zero divided by zero?

That’s the trigger for Adrian’s investigation of the calculus – the tool we use to reckon with very small quantities. It plays a huge part in many aspects of modern-day design, medicine and statistical work.

However, what is less well-known is the 17th century row between two eminent scientists as to who actually invented it. Adrian meets science writer, Brian Clegg, to find out about the race to claim credit.

It didn’t just cause a storm at its inception - we hear about the disagreements that dogged the calculus’s early days, with the church too getting involved in the disputes about the infinitely small.

But as Adrian discovers, the quest to understand the infinite has left us with a branch of mathematics of unparalleled importance.

Producer: Philippa Goodrich

A Juniper production for BBC Radio 4, first broadcast in September 2016.

Having looked at the infinite in philosophical and theological terms, it’s time to view it through the lens of mathematics.

Adrian Moore introduces us to the pivotal role mathematics has played in the quest to understand the infinite.

He begins by enlisting the help of very modern technology and considering the real question put by an 11 year old boy - what is zero divided by zero?

But as Adrian discovers, the quest to understand the infinite has left us with a branch of mathematics of unparalleled importance.

Producer: Philippa Goodrich

A Juniper production for BBC Radio 4, first broadcast in September 2016.

Previous Episode

4. The Infinite and Human Experience

Adrian Moore continues his journey through philosophical thought on infinity over the last two and a half thousand years.

He brings us to the verge of the modern world and the way we think now. He leaves the arguments of the medieval church and renaissance thinkers behind and steps into the world of enlightenment philosophy, as heralded by Rene Descartes.

Adrian tells us that Descartes was a typical enlightenment philosopher, seeking to establish what understanding we can have of the infinite using our own finite intellectual resources. How can we have any sense of infinity, if we have no direct experience of it?

Adrian describes Descartes’ attempts to establish a secure foundation for his beliefs, beginning with his questioning of his own existence and then of the existence of God.

We also meet the British empiricists who took issue with Descartes, and finally Immanuel Kant, who believed that each human being is of infinite worth.

The soundtrack is Beethoven’s eighth string quartet, which is said to have been inspired by Kant’s vision of our place as human beings in the universe.

Producer: Philippa Goodrich

A Juniper production for BBC Radio 4, first broadcast in September 2016.

Next Episode

6. The Mathematics of the Infinitely Big

Adrian Moore continues his exploration of two and a half millennia of philosophical thought on infinity.

Discover the brilliant but tortured German mathematician, Georg Cantor, who devised a way of distinguishing between infinitely big numbers and of performing calculations with them.

His work was revolutionary but, as Adrian discovers, it greatly polarised opinion amongst his late 19th and early 20th century contemporaries.

We hear how Cantor himself suffered a complete breakdown in his mental health.

As Adrian takes us with him deep into the world of infinite set theory, he enlists the help of Mary Leng, Senior Lecturer in Philosophy at York University, and four very familiar twentieth century friends.

Producer: Philippa Goodrich

A Juniper production for BBC Radio 4, first broadcast in September 2016.